3D Computer Vision (2024/25)

Exercise

Upload: 30.10.2024 (11:30)

Deadline: 16.01.2025 (23:59)

Group 07

• Daiana Tei
• Ahsan Aftab
• Dhruv Kale

By submitting this exercise, we confirm the following:

• All people listed above contributed to this solution
• No other people were involved in this solution
• No contents of this solution were copied from others (this includes people, large language models, websites, etc.)

3D Scene Reconstruction

Task Overview

Your task in this exercise is to do a dense reconstruction of a scene. This will involve multiple steps that you will encounter and learn about as the semester progresses. You can start implementing individual steps as soon as you learn about them or wait until you have learned more to implement everything together. In the latter case, be mindful that this exercise is designed for an entire semester and the workload is accordingly large.

You will be given the following data:

• 9 color images of the scene.
  • 8 Bit RGB per pixel.
  • Each image rendered from a different position.
  • The camera used had lens distortion.
• 9 Depth images of the scene.
  • 8 Bit Grayscale per pixel. The result of dividing the Z-depth by each image's maximum and then multiplying by 255.
  • Each image has the same pose as the corresponding RGB image.
  • The camera used was free of any distortions.
• 1 Dictionary containing camera calibration parameters.
  • They belong to the camera that was used to render the RGB images.
  • Distortion coefficients are given in the standard [k₁, k₂, p₁, p₂, k₃] order.
• 1 Numpy array containing 8 camera transformations.
  • They specify the movements that the camera went through to render all images.
  • I.e. idx 0 specifies the transformation from 00.png to 01.png, idx 1 specifies the transformation from 01.png to 02.png, ...
  • This applies to both RGB and Depth images, as they have the same poses.
• 1 Numpy array containing 7 features.
  • The features are specified for each of the 9 images.
  • Each feature is a 2D pixel location in "H, W" order, meaning the first value is the height/row in the image and the second width/column.
  • If a feature was not visible, it was entered as [-1, -1].
  • The features are unsorted, meaning that feature idx 0 for 00.png could be corresponding to e.g. feature idx 4 for 01.png.

Solution requirements

• Your code needs to compile, run, and produce an output.
• Your target output should be a dense point cloud reconstruction (without holes) of the scene.
  • The output should be in the .ply format. We provide a function that can exports a .ply file.
  • You may inspect your .ply outputs in e.g. Meshlab.
  • See the 'Dense Point Cloud' sample image to get an idea of what is possible. (Meshlab screenshot with point shading set to None)
• Your code should be a general solution.
  • This means that it could run correctly for a different dataset (with same input structure).
  • It should NOT include anything hardcoded specific to this dataset.
• Your code should not be unnecessarily inefficient.
  • Our sample solution runs in less than 2 minutes total (including point cloud export).
  • If your solution runs for more than 10 minutes, you are being wasteful in some part of your program.

Environment setup

!python --version

Python 3.11.11

!pip install numpy
!pip install pandas
!pip install matplotlib
!pip install scikit-learn
!pip3 install opencv-python
!pip install scipy
!pip install torch
!pip install torchvision
!pip3 install open3d-python

Requirement already satisfied: numpy in /Users/ahsanaftab/Semester-3/3D-Computer vision/project/.venv/lib/python3.11/site-packages (2.2.1)

[notice] A new release of pip is available: 23.2.1 -> 24.3.1
[notice] To update, run: pip install --upgrade pip
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[notice] A new release of pip is available: 23.2.1 -> 24.3.1
[notice] To update, run: pip install --upgrade pip
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[notice] A new release of pip is available: 23.2.1 -> 24.3.1
[notice] To update, run: pip install --upgrade pip
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[notice] A new release of pip is available: 23.2.1 -> 24.3.1
[notice] To update, run: pip install --upgrade pip
Requirement already satisfied: opencv-python in /Users/ahsanaftab/Semester-3/3D-Computer vision/project/.venv/lib/python3.11/site-packages (4.10.0.84)
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[notice] A new release of pip is available: 23.2.1 -> 24.3.1
[notice] To update, run: pip install --upgrade pip
Requirement already satisfied: scipy in /Users/ahsanaftab/Semester-3/3D-Computer vision/project/.venv/lib/python3.11/site-packages (1.15.1)
Requirement already satisfied: numpy<2.5,>=1.23.5 in /Users/ahsanaftab/Semester-3/3D-Computer vision/project/.venv/lib/python3.11/site-packages (from scipy) (2.2.1)

[notice] A new release of pip is available: 23.2.1 -> 24.3.1
[notice] To update, run: pip install --upgrade pip
Requirement already satisfied: torch in /Users/ahsanaftab/Semester-3/3D-Computer vision/project/.venv/lib/python3.11/site-packages (2.5.1)
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[notice] A new release of pip is available: 23.2.1 -> 24.3.1
[notice] To update, run: pip install --upgrade pip
Requirement already satisfied: torchvision in /Users/ahsanaftab/Semester-3/3D-Computer vision/project/.venv/lib/python3.11/site-packages (0.20.1)
Requirement already satisfied: numpy in /Users/ahsanaftab/Semester-3/3D-Computer vision/project/.venv/lib/python3.11/site-packages (from torchvision) (2.2.1)
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Requirement already satisfied: networkx in /Users/ahsanaftab/Semester-3/3D-Computer vision/project/.venv/lib/python3.11/site-packages (from torch==2.5.1->torchvision) (3.4.2)
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Requirement already satisfied: sympy==1.13.1 in /Users/ahsanaftab/Semester-3/3D-Computer vision/project/.venv/lib/python3.11/site-packages (from torch==2.5.1->torchvision) (1.13.1)
Requirement already satisfied: mpmath<1.4,>=1.1.0 in /Users/ahsanaftab/Semester-3/3D-Computer vision/project/.venv/lib/python3.11/site-packages (from sympy==1.13.1->torch==2.5.1->torchvision) (1.3.0)
Requirement already satisfied: MarkupSafe>=2.0 in /Users/ahsanaftab/Semester-3/3D-Computer vision/project/.venv/lib/python3.11/site-packages (from jinja2->torch==2.5.1->torchvision) (3.0.2)

[notice] A new release of pip is available: 23.2.1 -> 24.3.1
[notice] To update, run: pip install --upgrade pip
Requirement already satisfied: open3d-python in /Users/ahsanaftab/Semester-3/3D-Computer vision/project/.venv/lib/python3.11/site-packages (0.3.0.0)
Requirement already satisfied: numpy in /Users/ahsanaftab/Semester-3/3D-Computer vision/project/.venv/lib/python3.11/site-packages (from open3d-python) (2.2.1)

[notice] A new release of pip is available: 23.2.1 -> 24.3.1
[notice] To update, run: pip install --upgrade pip

Imports

Please note the following:

• These are all imports necessary to achieve the sample results.
• You may remove and/or add other libraries at your own convinience.
• Using library functions (from the given or other libraries) that bypass necessary computer vision tasks will not be recognized as 'solved'.
  • E.g.: If you need to undistort an image to get to the next step of the solution and use the library function cv2.undistort(), then we will evaluate the undistortion step as 'failed'.
  • E.g.: If you want to draw points in an image (to check your method or visualize in-between steps) and use the library function cv2.circle(), then there is no problem.
  • E.g.: If you need to perform complex mathematical operations and use some numpy function, then there is no problem.
  • E.g.: You do not like a provided utility function and find/know a library function that gives the same outputs from the same inputs, then there is no problem.

import os
os.sys.path

import numpy as np
import pandas as pd
import matplotlib.pyplot as plt
import sklearn
import cv2
import open3d as o3d
import scipy
import torch
import torchvision

Data

This should load all available data and also create some output directories. Feel free to rename variables or add additional directories as you see fit.

#Inputs
base_path = os.getcwd()
data_path = os.path.join(base_path, f"data")
img_path = os.path.join(data_path, 'images')
depth_path = os.path.join(data_path, 'depths')
print(f"The project's root path is '{base_path}'.")
print(f"Reading data from '{data_path}'.")
print(f"Image folder: '{img_path}'.")
print(f"Depth folder: '{depth_path}'.")

#Outputs
out_path = os.path.join(base_path, 'output')
ply_path = os.path.join(out_path, 'point_cloud')
os.makedirs(out_path, exist_ok=True)
os.makedirs(ply_path, exist_ok=True)
print(f"\nCreating directory '{out_path}'.")
print(f"Creating directory '{ply_path}'.")

#Load Data
camera_calibration = np.load(os.path.join(data_path, 'camera_calibration.npy'), allow_pickle=True)
camera_calibration = camera_calibration.item()#get dictionary from numpy array struct
given_features = np.load(os.path.join(data_path, 'given_features.npy'), allow_pickle=True)
camera_movement = np.load(os.path.join(data_path, 'camera_movement.npy'), allow_pickle=True)

print(f"\nCamera Calibration:")
for entry in camera_calibration.items():
    print(f"  {entry[0]}: {entry[1]}")
print(f"Camera Movement: {camera_movement.shape}")#[Cameras-1, 4, 4]
print(f"2D Features (Unsorted): {given_features.shape}")#[Camera_idx, Feature_idx, 2]

The project's root path is '/Users/ahsanaftab/Semester-3/3D-Computer vision/project/3D-Scene-Reconstruction'.
Reading data from '/Users/ahsanaftab/Semester-3/3D-Computer vision/project/3D-Scene-Reconstruction/data'.
Image folder: '/Users/ahsanaftab/Semester-3/3D-Computer vision/project/3D-Scene-Reconstruction/data/images'.
Depth folder: '/Users/ahsanaftab/Semester-3/3D-Computer vision/project/3D-Scene-Reconstruction/data/depths'.

Creating directory '/Users/ahsanaftab/Semester-3/3D-Computer vision/project/3D-Scene-Reconstruction/output'.
Creating directory '/Users/ahsanaftab/Semester-3/3D-Computer vision/project/3D-Scene-Reconstruction/output/point_cloud'.

Camera Calibration:
  distortion_param: [-0.1, 0.02, 0.0, 0.0, -0.01]
  image_height: 551
  image_width: 881
  principal_point: [275.0, 440.0]
  focal_length_mm: 25
  sensor_width_mm: 35
  pixel_ratio: 1.0
  pixel_per_mm: 25.17142857142857
  focal_length_px: 629.2857142857142
Camera Movement: (8, 4, 4)
2D Features (Unsorted): (9, 7, 2)

import glob
rgb_paths = sorted(glob.glob("data/images/*.png"))
depth_paths = sorted(glob.glob("data/depths/*.png"))
feature_data = np.load("data/given_features.npy")

output_folder = "output"

for i in range(len(rgb_paths)):
    rgb_image = cv2.imread(rgb_paths[i])
    depth_map = cv2.imread(depth_paths[i], cv2.IMREAD_GRAYSCALE)
    features = feature_data[i]
    
    plt.figure(figsize=(15, 5))
    plt.subplot(1, 3, 1)
    plt.imshow(cv2.cvtColor(rgb_image, cv2.COLOR_BGR2RGB))
    plt.title(f"RGB Image {i}")
    
    plt.subplot(1, 3, 2)
    plt.imshow(depth_map, cmap="jet_r")
    plt.colorbar()
    plt.title(f"Depth Map {i}")

    plt.subplot(1, 3, 3)
    plt.imshow(cv2.cvtColor(rgb_image, cv2.COLOR_BGR2RGB))
    for feature in features:
        if feature[0] != -1:  # invalid features: if feature is not visible in image, coordinates are [-1, -1]
            plt.plot(feature[1], feature[0], 'ro', markersize=2)
    plt.title(f"Features {i}")

    plt.tight_layout()
    plt.show()

--- Data visualisation prepared by Daiana Tei

Undistortion

focal_length_px = camera_calibration['focal_length_px']
principal_point = camera_calibration['principal_point']
coeffs = camera_calibration['distortion_param']

K = np.array([
    [focal_length_px, 0, principal_point[1]],  
    [0, focal_length_px, principal_point[0]],  
    [0, 0, 1]                                 
], dtype=np.float64)

print("Camera matrix K:")
print(K)
print("\nDistortion coefficients:")
print(coeffs)

Camera matrix K:
[[629.28571429   0.         440.        ]
 [  0.         629.28571429 275.        ]
 [  0.           0.           1.        ]]

Distortion coefficients:
[-0.1, 0.02, 0.0, 0.0, -0.01]

def undistort_image_inverse_sampling(image, file_name, K, distortion_params):
    h, w = image.shape[:2]
    f_x, f_y = K[0, 0], K[1, 1]
    u_0, v_0 = K[0, 2], K[1, 2]

    # empty output
    undistorted = np.zeros_like(image)
    # grid of undistorted coordinates
    u_grid, v_grid = np.meshgrid(np.arange(w), np.arange(h))
    undistorted_coords = np.stack([u_grid.ravel(), v_grid.ravel()], axis=-1)
    distorted_coords = []
    
    # for each coordinate, calculate corresponding distorted coordinates
    for u, v in undistorted_coords:
        # normalisation
        x = (u - u_0) / f_x
        y = (v - v_0) / f_y
        # invert distortion model
        x_dist, y_dist = x, y
        
        r2 = x_dist**2 + y_dist**2
        radial_distortion = 1 + distortion_params[0]*r2 + distortion_params[1]*r2**2 + distortion_params[4]*r2**3
        tangential_x = 2 * distortion_params[2] * x_dist * y_dist + distortion_params[3] * (r2 + 2 * x_dist**2)
        tangential_y = distortion_params[2] * (r2 + 2 * y_dist**2) + 2 * distortion_params[3] * x_dist * y_dist

        x_dist = x * radial_distortion + tangential_x
        y_dist = y * radial_distortion + tangential_y

        # map distorted normalized coordinates back to pixels
        u_dist = f_x * x_dist + u_0
        v_dist = f_y * y_dist + v_0
        distorted_coords.append((u_dist, v_dist))

    distorted_coords = np.array(distorted_coords).reshape(h, w, 2)
    # bilinear interpolation to sample distorted image
    map_x = distorted_coords[:, :, 0].astype(np.float32)
    map_y = distorted_coords[:, :, 1].astype(np.float32)
    undistorted = cv2.remap(image, map_x, map_y, interpolation=cv2.INTER_LINEAR, borderMode=cv2.BORDER_CONSTANT)
    
    os.makedirs(output_folder, exist_ok=True)
    output_path = os.path.join(output_folder, file_name)
    cv2.imwrite(output_path, undistorted)
    print(f"Saved undistorted image to {output_path}")
    return undistorted

for i in range(len(rgb_paths)):
    distorted_image = cv2.imread(rgb_paths[i])
    undistorted_image = undistort_image_inverse_sampling(distorted_image, f"{i}.png", K, coeffs)
    
    plt.figure(figsize=(20, 10))
    plt.subplot(1, 2, 1)
    plt.imshow(cv2.cvtColor(distorted_image, cv2.COLOR_BGR2RGB))
    plt.title("Distorted Image")
    plt.subplot(1, 2, 2)
    plt.imshow(cv2.cvtColor(undistorted_image, cv2.COLOR_BGR2RGB))
    plt.title("Undistorted Image")
    plt.show()

undistorted_images = sorted(glob.glob(output_folder+"/*.png"))

Saved undistorted image to output/0.png

Saved undistorted image to output/1.png

Saved undistorted image to output/2.png

Saved undistorted image to output/3.png

Saved undistorted image to output/4.png

Saved undistorted image to output/5.png

Saved undistorted image to output/6.png

Saved undistorted image to output/7.png

Saved undistorted image to output/8.png

--- Undistortion prepared by Daiana Tei

Matching features

Data observation

print(feature_data)

[[[163 616]
  [431 593]
  [380 672]
  [164 660]
  [378 462]
  [280 422]
  [274 650]]

 [[192 722]
  [183 694]
  [398 444]
  [495 651]
  [495 446]
  [346 704]
  [282 376]]

 [[252 536]
  [384 621]
  [291 480]
  [157 501]
  [ -1  -1]
  [ -1  -1]
  [157 540]]

 [[ -1  -1]
  [199 614]
  [ -1  -1]
  [307 657]
  [195 658]
  [409 690]
  [285 422]]

 [[168 693]
  [474 681]
  [ -1  -1]
  [285 374]
  [157 722]
  [322 722]
  [473 446]]

 [[285 481]
  [207 500]
  [ -1  -1]
  [ -1  -1]
  [207 539]
  [ -1  -1]
  [303 539]]

 [[187 650]
  [448 574]
  [284 636]
  [386 649]
  [313 424]
  [177 610]
  [383 460]]

 [[ -1  -1]
  [ -1  -1]
  [ -1  -1]
  [ -1  -1]
  [444 367]
  [ -1  -1]
  [505 444]]

 [[472 485]
  [350 602]
  [473 631]
  [259 554]
  [ -1  -1]
  [ -1  -1]
  [ -1  -1]]]

for i in range(len(undistorted_images)):
    rgb_image = cv2.imread(undistorted_images[i])
    features = feature_data[i]
    
    plt.imshow(cv2.cvtColor(rgb_image, cv2.COLOR_BGR2RGB))
    for feature in features:
        if feature[0] != -1:  # invalid features: if feature is not visible in image, coordinates are [-1, -1]
            plt.plot(feature[1], feature[0], 'ro', markersize=2)
    plt.title(f"Features {i}")

    plt.tight_layout()
    plt.show()

print(camera_movement)

[[[ 7.07106781e-01 -1.83012702e-01  6.83012702e-01 -3.00000000e+00]
  [ 1.83012702e-01  9.80379875e-01  7.32233047e-02 -2.58819045e-01]
  [-6.83012702e-01  7.32233047e-02  7.26726907e-01  9.65925826e-01]
  [ 0.00000000e+00  0.00000000e+00  0.00000000e+00  1.00000000e+00]]

 [[ 6.12323400e-17  2.58819045e-01 -9.65925826e-01  4.00000000e+00]
  [-2.58819045e-01  9.33012702e-01  2.50000000e-01 -1.03527618e+00]
  [ 9.65925826e-01  2.50000000e-01  6.69872981e-02  3.86370331e+00]
  [ 0.00000000e+00  0.00000000e+00  0.00000000e+00  1.00000000e+00]]

 [[ 7.07106781e-01 -1.83012702e-01  6.83012702e-01 -2.82842712e+00]
  [ 1.29893408e-16  9.65925826e-01  2.58819045e-01 -1.00000000e+00]
  [-7.07106781e-01 -1.83012702e-01  6.83012702e-01  1.41421356e+00]
  [ 0.00000000e+00  0.00000000e+00  0.00000000e+00  1.00000000e+00]]

 [[ 7.07106781e-01 -1.29893408e-16  7.07106781e-01 -3.00000000e+00]
  [ 1.29893408e-16  1.00000000e+00  5.38036114e-17 -2.22044605e-16]
  [-7.07106781e-01  5.38036114e-17  7.07106781e-01  1.00000000e+00]
  [ 0.00000000e+00  0.00000000e+00  0.00000000e+00  1.00000000e+00]]

 [[ 6.12323400e-17  1.83697020e-16 -1.00000000e+00  4.00000000e+00]
  [-1.83697020e-16  1.00000000e+00  1.83697020e-16 -7.77156117e-16]
  [ 1.00000000e+00  1.83697020e-16  6.12323400e-17  4.00000000e+00]
  [ 0.00000000e+00  0.00000000e+00  0.00000000e+00  1.00000000e+00]]

 [[ 7.07106781e-01 -2.08398031e-16  7.07106781e-01 -2.82842712e+00]
  [ 2.98836239e-01  9.06307787e-01 -2.98836239e-01  1.21494310e+00]
  [-6.40856382e-01  4.22618262e-01  6.40856382e-01  2.12694929e+00]
  [ 0.00000000e+00  0.00000000e+00  0.00000000e+00  1.00000000e+00]]

 [[ 7.07106781e-01 -2.98836239e-01  6.40856382e-01 -3.00000000e+00]
  [ 5.00000000e-01  8.52165513e-01 -1.54317655e-01  1.41421356e+00]
  [-5.00000000e-01  4.29547251e-01  7.51990132e-01  0.00000000e+00]
  [ 0.00000000e+00  0.00000000e+00  0.00000000e+00  1.00000000e+00]]

 [[ 6.12323400e-17  7.07106781e-01 -7.07106781e-01  2.00000000e+00]
  [-7.07106781e-01  5.00000000e-01  5.00000000e-01 -1.41421356e+00]
  [ 7.07106781e-01  5.00000000e-01  5.00000000e-01  1.41421356e+00]
  [ 0.00000000e+00  0.00000000e+00  0.00000000e+00  1.00000000e+00]]]

Camera transformations visualisation

import numpy as np
import matplotlib.pyplot as plt
from mpl_toolkits.mplot3d import Axes3D

def look_at(eye, target, up):
    eye = np.array(eye, dtype=np.float64)  
    target = np.array(target, dtype=np.float64)
    up = np.array(up, dtype=np.float64)
    
    forward = target - eye
    forward /= np.linalg.norm(forward) 
    right = np.cross(up, forward)
    right /= np.linalg.norm(right) 
    up = np.cross(forward, right)

    rotation_matrix = np.eye(4)
    rotation_matrix[:3, 0] = right
    rotation_matrix[:3, 1] = up
    rotation_matrix[:3, 2] = -forward

    translation_matrix = np.eye(4)
    translation_matrix[:3, 3] = -eye
    return rotation_matrix @ translation_matrix

# Initial position
eye = [0, 0, 0]
target = [1, 1, 0]
up = [0, 0, 1]
initial_pose = look_at(eye, target, up)

camera_poses = [initial_pose]
current_pose = initial_pose.copy()
for transform in camera_movement:
    current_pose = current_pose @ transform
    camera_poses.append(current_pose)

camera_positions = np.array([pose[:3, 3] for pose in camera_poses])
camera_rotations = np.array([pose[:3, :3] for pose in camera_poses])
fig = plt.figure()
ax = fig.add_subplot(111, projection='3d')
ax.scatter(camera_positions[:, 0], camera_positions[:, 1], camera_positions[:, 2], c='r')

for i, (pose, R) in enumerate(zip(camera_positions, camera_rotations)):
    x_axis = R[:, 0]
    y_axis = R[:, 1]
    z_axis = R[:, 2]
    start = pose
    length = 0.5
    ax.quiver(start[0], start[1], start[2], x_axis[0], x_axis[1], x_axis[2], color='r', length=length)
    ax.quiver(start[0], start[1], start[2], y_axis[0], y_axis[1], y_axis[2], color='g', length=length)
    ax.quiver(start[0], start[1], start[2], z_axis[0], z_axis[1], z_axis[2], color='b', length=length)
    ax.text(start[0], start[1], start[2], f' {i}', None)

ax.set_xlabel('X')
ax.set_ylabel('Y')
ax.set_zlabel('Z')
plt.show()

--- Visualisation prepared by Daiana Tei

Feature matching

Computing fundamental matrices

def get_essential_matrix(R, t):
    """
    Computes essential matrix E (3x3) from rotation matrix (3x3) and translation vector (3,).
    """
    # Skew-symmetric matrix for t
    t_skew = np.array([
        [0, -t[2], t[1]],
        [t[2], 0, -t[0]],
        [-t[1], t[0], 0]
    ])
    # E = [t]_x R
    E = t_skew @ R
    return E
    
def get_fundamental_matrix(E, K):
    """
    Computes fundamental matrix F (3x3) from essential matrix E (3x3) and camera matrix K (3x3).
    """
    # F = K^-T E K^-1
    F = np.linalg.inv(K).T @ E @ np.linalg.inv(K)
    # Normalisation
    F = F / F[2, 2]
    return F

num_images = len(undistorted_images)

F = []
for i in range(num_images-1):
    R = camera_movement[i][:3, :3]
    t = camera_movement[i][:3, 3]
    E = get_essential_matrix(R, t)
    F.append(get_fundamental_matrix(E, K))

print(F)

[array([[-4.28363670e-22,  9.93913280e-06, -1.05735875e-03],
       [ 1.40560564e-05, -4.41360389e-07, -2.44523175e-02],
       [-1.49533109e-03,  1.50993082e-02,  1.00000000e+00]]), array([[ 6.96713717e-22,  1.06817758e-05, -1.13636364e-03],
       [ 1.06817758e-05, -6.13874952e-22,  2.25903012e-03],
       [-1.13636364e-03, -1.16589928e-02,  1.00000000e+00]]), array([[-6.56430105e-06,  1.09822897e-05,  5.99649959e-03],
       [ 9.28332357e-06,  7.20810283e-06, -2.29953094e-02],
       [-3.79544239e-03,  1.02149656e-02,  1.00000000e+00]]), array([[-1.03326556e-22,  3.81056112e-06, -1.04790431e-03],
       [ 5.38894722e-06, -1.20099078e-22, -9.15351177e-03],
       [-1.48196048e-03,  5.51714814e-03,  1.00000000e+00]]), array([[ 4.37686340e-23,  4.13223140e-06, -1.13636364e-03],
       [ 4.13223140e-06, -0.00000000e+00,  7.82172373e-04],
       [-1.13636364e-03, -4.41853601e-03,  1.00000000e+00]]), array([[ 3.16127319e-06,  3.16127319e-06, -4.24965438e-03],
       [ 6.89910318e-07, -2.67202356e-06, -4.23413869e-03],
       [ 8.16760564e-04,  2.94976229e-03,  1.00000000e+00]]), array([[-1.31878981e-05,  1.13296507e-05,  1.51684870e-02],
       [-2.79757564e-05,  2.40338186e-05,  3.21772201e-02],
       [-1.58452316e-02, -3.66386001e-02,  1.00000000e+00]]), array([[-4.57578416e-22, -3.20747801e-06, -1.13636364e-03],
       [-3.20747801e-06, -2.51801851e-22, -1.44318674e-03],
       [-1.13636364e-03,  4.26576739e-03,  1.00000000e+00]])]

Projecting epipolar lines

colors = ['r', 'g', 'b', 'c', 'm', 'y', 'k'] # Matplotlib color codes

for i in range(num_images-1):
    img1 = cv2.cvtColor(cv2.imread(undistorted_images[i]), cv2.COLOR_BGR2RGB)
    img2 = cv2.cvtColor(cv2.imread(undistorted_images[i+1]), cv2.COLOR_BGR2RGB)
    
    fig, axs = plt.subplots(1, 2, figsize=(10, 5))
    # Features in first image
    axs[0].imshow(img1)
    k = 0
    for p1 in feature_data[i]:
        if p1[0] == -1:
            continue
        axs[0].plot(p1[1], p1[0], colors[k] + 'o', markersize=3) # height is x, width is y
        k += 1

    axs[1].imshow(img2)
    # Epipolar lines from features in second image using respective colours
    k = 0
    for p1 in feature_data[i]:
        if p1[0] == -1:
            continue
        x1 = np.array([p1[1], p1[0], 1])  # homogeneous coordinates
        l2 = F[i] @ x1  # epipolar line
        l2 = [l2[0]/l2[2], l2[1]/l2[2], 1.0]
        
        h, w = img2.shape[:2]
        x0, y0 = 0, -l2[2] / l2[1]
        x1, y1 = h, -(l2[2] + l2[0] * h) / l2[1]
        axs[1].axline((x1, y1), (x0, y0), color=colors[k])
        k += 1

    # Features in second image
    for p1 in feature_data[i+1]:
        if p1[0] == -1:
            continue
        axs[1].plot(p1[1], p1[0], 'ro', markersize=3) 

    plt.show()

--- Feature matching prepared by Daiana Tei

Finding correspondences between consecutive images

num_features = len(feature_data[0])

def match_feature_(feature, features_to_match, F, distance_threshold=2):
    """
    Matches feature to that of another view.
    """
    if feature[0] == -1:
        return -1

    x1 = np.array([feature[1], feature[0], 1])
    epipolar_line = F @ x1
    epipolar_line = [epipolar_line[0]/epipolar_line[2], epipolar_line[1]/epipolar_line[2], 1.0]
    best_match = -1
    min_distance = float('inf')

    for l in range(len(features_to_match)):
        if features_to_match[l, 0] != -1:
            x2 = np.array([features_to_match[l, 1], features_to_match[l, 0], 1])
            distance = np.abs(epipolar_line[0] * x2[0] + epipolar_line[1] * x2[1] + epipolar_line[2]) / np.sqrt(epipolar_line[0]**2 + epipolar_line[1]**2)
            if distance < min_distance:
                min_distance = distance
                best_match = l

    if min_distance < distance_threshold:
        return best_match
    return -1

matches = []
for i in range(num_images-1):
    matches_i = []
    for j in range(num_features):
        match = match_feature_(feature_data[i, j], feature_data[i+1], F[i])
        if match != -1:
            matches_i.append((j, match))
    matches.append(matches_i)
    print(f"{i}->{i+1}", matches_i)

0->1 [(0, 1), (1, 4), (2, 3), (3, 0), (4, 2), (5, 6), (6, 5)]
1->2 [(0, 6), (1, 3), (4, 1), (5, 0), (6, 2)]
2->3 [(0, 3), (2, 6), (3, 1), (6, 4)]
3->4 [(1, 0), (3, 5), (4, 4), (5, 1), (6, 3)]
4->5 [(0, 1), (3, 0), (4, 4), (5, 6)]
5->6 [(0, 4), (1, 5), (4, 0), (6, 2)]
6->7 [(4, 4), (6, 6)]
7->8 [(4, 0)]

for i in range(num_images-1):
    img1 = cv2.cvtColor(cv2.imread(undistorted_images[i]), cv2.COLOR_BGR2RGB)
    img2 = cv2.cvtColor(cv2.imread(undistorted_images[i+1]), cv2.COLOR_BGR2RGB)

    fig, axs = plt.subplots(1, 2, figsize=(10, 5))
    axs[0].imshow(img1)
    for j, (match1, match2) in enumerate(matches[i]):
        u1, v1 = feature_data[i, match1]
        axs[0].plot(v1, u1, colors[j] + 'o', markersize=3) # Note: v1 is x, u1 is y for plotting

    axs[1].imshow(img2)
    for j, (match1, match2) in enumerate(matches[i]):
        u2, v2 = feature_data[i+1, match2]
        axs[1].plot(v2, u2, colors[j] + 'o', markersize=3)  # Note: v2 is x, u2 is y

    axs[0].set_title(f"Image {i}")
    axs[1].set_title(f"Image {i+1}")
    plt.tight_layout()
    plt.show()

--- Feature matching prepared by Daiana Tei

Visualising all correspondences

def get_transformation_matrices(view_idx):
    """
    Calculates transformation matrices from the given view to all views
    """
    pose = np.eye(4)
    transformations = [pose]
    for i in range(num_images-1 - view_idx):
        pose = camera_movement[i+view_idx] @ pose
        transformations.append(pose)

    pose = np.eye(4)
    for i in range(view_idx):
        pose = np.linalg.inv(camera_movement[view_idx-1-i]) @ pose
        transformations.insert(0, pose)
    return transformations

def show_features_from_view(idx):
    transformations = get_transformation_matrices(idx)
    for i in range(num_images):
        if i == idx:
            continue
        
        img1 = cv2.cvtColor(cv2.imread(undistorted_images[idx]), cv2.COLOR_BGR2RGB)
        img2 = cv2.cvtColor(cv2.imread(undistorted_images[i]), cv2.COLOR_BGR2RGB)
        fig, axs = plt.subplots(1, 2, figsize=(10, 5))
        
        axs[0].imshow(img1)
        k = 0
        for p1 in feature_data[idx]:
            if p1[0] == -1:
                continue    
            axs[0].plot(p1[1], p1[0], colors[k] + 'o', markersize=3) # height is x, width is y
            k += 1
    
        R = transformations[i][:3, :3]
        t = transformations[i][:3, 3]
        E = get_essential_matrix(R, t)
        F = get_fundamental_matrix(E, K)
        
        axs[1].imshow(img2)
        k = 0
        bad_pair = False
        for p1 in feature_data[idx]:
            if p1[0] == -1:
                continue
            
            x1 = np.array([p1[1], p1[0], 1])
            l2 = F @ x1
            l2 = [l2[0]/l2[2], l2[1]/l2[2], 1.0]
            
            h, w = img2.shape[:2]
            x0, y0 = 0, -l2[2] / l2[1]
            x1, y1 = h, -(l2[2] + l2[0] * h) / l2[1]
            axs[1].axline((x1, y1), (x0, y0), color=colors[k])
            k += 1
    
            if abs(y0) > (h+w) * 2 or abs(y1) > (h+w) * 2:
                bad_pair = True
                break
    
        if bad_pair == True:
            print(f"! ! ! BAD VIEWS between images {idx} and {i}")
            continue
    
        for p1 in feature_data[i]:
            if p1[0] == -1:
                continue
            axs[1].plot(p1[1], p1[0], 'ro', markersize=3) 
    
        axs[0].set_title(f"Image {idx}")
        axs[1].set_title(f"Image {i}")
        plt.show()

for i in range(num_images):
    show_features_from_view(i)

! ! ! BAD VIEWS between images 0 and 3

! ! ! BAD VIEWS between images 0 and 6

! ! ! BAD VIEWS between images 1 and 4

! ! ! BAD VIEWS between images 1 and 7

! ! ! BAD VIEWS between images 2 and 5

! ! ! BAD VIEWS between images 2 and 8
! ! ! BAD VIEWS between images 3 and 0

! ! ! BAD VIEWS between images 3 and 6

! ! ! BAD VIEWS between images 4 and 1

! ! ! BAD VIEWS between images 4 and 7

! ! ! BAD VIEWS between images 5 and 2

! ! ! BAD VIEWS between images 5 and 8
! ! ! BAD VIEWS between images 6 and 0

! ! ! BAD VIEWS between images 6 and 3

! ! ! BAD VIEWS between images 7 and 1

! ! ! BAD VIEWS between images 7 and 4

! ! ! BAD VIEWS between images 8 and 2

! ! ! BAD VIEWS between images 8 and 5

Building correspondence matrix

feature_correspondence_matrix = []
features_matched = []

for i in range(num_images):
    feature = []
    matches = []
    for j in range(num_features):
        feature.append([-1, -1])
        matches.append(False)
    feature_correspondence_matrix.append(feature)
    features_matched.append(matches)

for i in range(num_features):
    feature_correspondence_matrix[0][i] = feature_data[0][i]
    features_matched[0][i] = True

h, w = img2.shape[:2]
ambig_param = 1.1

def match_feature(feature, features_to_match, F, distance_threshold=5):
    """
    Matches feature to that of another view, or returns (1, [-1, -1]) if feature was not found, (0, [-1, -1]) and (0, [0, 0]) in case of bad view or ambiguity respectively.
    """
    if feature[0] == -1:
        return (1, [-1, -1])

    x1 = np.array([feature[1], feature[0], 1])
    epipolar_line = F @ x1
    epipolar_line = [epipolar_line[0]/epipolar_line[2], epipolar_line[1]/epipolar_line[2], 1.0]

    x0, y0 = 0, -epipolar_line[2] / epipolar_line[1]
    x1, y1 = h, -(epipolar_line[2] + epipolar_line[0] * h) / epipolar_line[1]
    if abs(y0) > (h+w) * 2 or abs(y1) > (h+w) * 2:
        return (0, [-1, -1])
    
    best_match = -1
    min_distance = float('inf')
    ambiguity = False
    
    for l in range(len(features_to_match)):
        if features_to_match[l, 0] != -1:
            x2 = np.array([features_to_match[l, 1], features_to_match[l, 0], 1])
            distance = np.abs(epipolar_line[0] * x2[0] + epipolar_line[1] * x2[1] + epipolar_line[2]) / np.sqrt(epipolar_line[0]**2 + epipolar_line[1]**2)
            if abs(distance-min_distance) < ambig_param:
                ambiguity = True
                
            if distance < min_distance:
                if abs(distance-min_distance) >= ambig_param:
                    ambiguity = False
                min_distance = distance
                best_match = l

    if ambiguity:
        return (0, [0, 0])
    if min_distance < distance_threshold:
        return (1, features_to_match[best_match])
        
    return (1, [-1, -1])

def find_missing_correspondences(view_idx):
    transformations = get_transformation_matrices(view_idx)
    for i in range(num_images):
        if i == view_idx:
            continue

        images_matched = True
        for j in range(num_features):
            if features_matched[i][j] == False:
                images_matched = False
        if images_matched:
            continue
        
        R = transformations[i][:3, :3]
        t = transformations[i][:3, 3]
        E = get_essential_matrix(R, t)
        F = get_fundamental_matrix(E, K)

        correspondences = []
        matched = []
        bad_view = False
        
        for j in range(num_features):
            feature = match_feature(feature_correspondence_matrix[view_idx][j], feature_data[i], F)
            if feature[0] == 0 and feature[1][0] == -1:
                bad_view = True
                break
            elif feature[0] == 0:
                correspondences.append([-1, -1])
                matched.append(False)
            else:
                correspondences.append(feature[1])
                matched.append(True)
        
        if bad_view:
            continue

        for j in range(num_features):
            if features_matched[i][j] == False:
                feature_correspondence_matrix[i][j] = correspondences[j]
                features_matched[i][j] = matched[j]

done = True
for i in range(num_images):
    find_missing_correspondences(i)
    done = True
    for k in range(num_images):
        for j in range(num_features):
            if features_matched[k][j] == False:
                done = False
                break
    if done:
        break    

for i in range(len(feature_correspondence_matrix)):
    print(feature_correspondence_matrix[i])

[array([163, 616], dtype=int32), array([431, 593], dtype=int32), array([380, 672], dtype=int32), array([164, 660], dtype=int32), array([378, 462], dtype=int32), array([280, 422], dtype=int32), array([274, 650], dtype=int32)]
[array([183, 694], dtype=int32), array([495, 446], dtype=int32), array([495, 651], dtype=int32), array([192, 722], dtype=int32), array([398, 444], dtype=int32), array([282, 376], dtype=int32), array([346, 704], dtype=int32)]
[array([157, 501], dtype=int32), array([384, 621], dtype=int32), [-1, -1], array([157, 540], dtype=int32), [-1, -1], array([291, 480], dtype=int32), array([252, 536], dtype=int32)]
[array([199, 614], dtype=int32), [-1, -1], array([409, 690], dtype=int32), array([195, 658], dtype=int32), [-1, -1], array([285, 422], dtype=int32), array([307, 657], dtype=int32)]
[array([168, 693], dtype=int32), array([473, 446], dtype=int32), array([474, 681], dtype=int32), array([157, 722], dtype=int32), [-1, -1], array([285, 374], dtype=int32), array([322, 722], dtype=int32)]
[array([207, 500], dtype=int32), [-1, -1], [-1, -1], array([207, 539], dtype=int32), [-1, -1], array([285, 481], dtype=int32), array([303, 539], dtype=int32)]
[array([177, 610], dtype=int32), array([448, 574], dtype=int32), array([386, 649], dtype=int32), array([187, 650], dtype=int32), array([383, 460], dtype=int32), array([313, 424], dtype=int32), array([284, 636], dtype=int32)]
[[-1, -1], [-1, -1], [-1, -1], [-1, -1], array([505, 444], dtype=int32), array([444, 367], dtype=int32), [-1, -1]]
[[-1, -1], array([473, 631], dtype=int32), array([350, 602], dtype=int32), [-1, -1], [-1, -1], array([472, 485], dtype=int32), array([259, 554], dtype=int32)]

Finally, see the result

for i in range(num_images):
    img = cv2.imread(undistorted_images[i])
    plt.imshow(cv2.cvtColor(img, cv2.COLOR_BGR2RGB))
    
    k = 0
    for feature in feature_correspondence_matrix[i]:
        if feature[0] != -1:
            plt.plot(feature[1], feature[0], colors[k] + 'o', markersize=5)
        k += 1
        
    plt.title(f"Image {i}")
    plt.tight_layout()
    plt.show()

--- Feature matching done by Daiana Tei

Triangulation

def get_projection_matrix(K, view_index):
    T = get_transformation_matrices(0)[view_index]
    P = K @ T[:3]
    return P

#Calculate all 3d points with multiview triangulation

def multiview_triangulation(features_matrix, projection_matrices):
    triangulated_points = []
    for feature_index, feature in enumerate(features_matrix):
        A = []
    
        for view_index, point in enumerate(feature):
            if np.array(point).sum() == -2:
                continue
            P = projection_matrices[view_index]
            #since points are (h,w) .ie (y,x)
            y, x = point
        
            A.append(x * P[2, :] - P[0, :])  # Row from x-coordinate
            A.append(y * P[2, :] - P[1, :])  # Row from y-coordinate

        A = np.array(A)  # Convert to NumPy array

    
        # Solve A * X = 0 using SVD
        _, _, Vt = np.linalg.svd(A)
        X_homogeneous = Vt[-1]  # Last row of Vt corresponds to smallest singular value
    
        # Convert to Euclidean coordinates
        X_euclidean = X_homogeneous[:-1] / X_homogeneous[-1]
        triangulated_points.append(X_euclidean)
    
    return triangulated_points

# Simulated 2D points from correspondence matrix and transposing shape from (9,7,2) to (7,9,2)
points_2d_all_features = np.array(feature_correspondence_matrix)
points_2d_all_features = np.transpose(points_2d_all_features, axes=(1, 0, 2))
    
# projection matrices for 9 views
projection_matrices = [get_projection_matrix(K, x) for x in range(0,9)]
     
        
# Perform multiview triangulation
points_3d = multiview_triangulation(points_2d_all_features, projection_matrices)

# Print results
for i, point in enumerate(points_3d):
   	print(f"Feature {i}: {point}")

Feature 0: [ 1.35201537 -0.86230485  4.81112929]
Feature 1: [0.90839178 0.92869221 3.73654327]
Feature 2: [1.63211365 0.744573   4.43802616]
Feature 3: [ 1.60153403 -0.8015058   4.58633108]
Feature 4: [0.1593758  0.72950708 4.45851857]
Feature 5: [-0.11231227  0.03941065  3.93977091]
Feature 6: [ 1.59977506e+00 -4.41454716e-03  4.80063840e+00]

#checking reprojection from 3d to 2d
for i in range(0, 7):
    a = np.hstack([points_3d[i], [1]])
    a = projection_matrices[0] @ a
    y, x, _ = a/a[-1]
    print(x, y)

162.21231786277394 616.8408014973934
431.40464923232537 592.9857748052221
380.57602276517207 671.4240079881464
165.02622389449078 659.7448171223541
377.96433206211844 462.4946720013839
281.29492490859474 422.06075682657115
274.4213245758087 649.7045239324775

#Sparse reconstruction 
def sparse_reconstruction(points_3d):
    point_cloud = o3d.geometry.PointCloud()
    point_cloud.points = o3d.utility.Vector3dVector(points_3d)
    point_cloud, ind = point_cloud.remove_statistical_outlier(nb_neighbors=20, std_ratio=2.0)
    return point_cloud

sparse_cloud = sparse_reconstruction(points_3d)    
o3d.visualization.draw_geometries([sparse_cloud])

def validate_triangulated_points(points_3d, points_2d_all_features, projection_matrices):
    """
    Validate triangulated 3D points by computing reprojection errors.

    Args:
        points_3d (list of numpy.ndarray): List of triangulated 3D points (N, 3).
        points_2d_all_features (numpy.ndarray): Correspondence matrix (features in 2D across views).
        projection_matrices (list of numpy.ndarray): List of 3x4 projection matrices.

    Returns:
        list: Reprojection errors for each feature.
    """
    reprojection_errors = []
    for feature_index, point_3d in enumerate(points_3d):
        total_error = 0
        for view_index, point_2d in enumerate(points_2d_all_features[feature_index]):
            if np.array(point_2d).sum() == -2:  # Skip invisible points
                continue
            point_3d_homogeneous = np.append(point_3d, 1)  # Convert to homogeneous
            reprojected_2d = projection_matrices[view_index] @ point_3d_homogeneous
            reprojected_2d /= reprojected_2d[2]  # Normalize by depth
            error = np.linalg.norm(reprojected_2d[:2] - point_2d)
            total_error += error
        reprojection_errors.append(total_error)
    return reprojection_errors

validate_triangulated_points(points_3d, points_2d_all_features, projection_matrices)

[np.float64(4205.211350852528),
 np.float64(1074.922959641321),
 np.float64(2051.879155461192),
 np.float64(4570.947531424286),
 np.float64(378.5354189274818),
 np.float64(1482.0943986012326),
 np.float64(3748.8880211216688)]

import open3d as o3d

def generate_sparse_point_cloud(points_3d):
    """
    Generate a sparse point cloud from triangulated 3D points.

    Args:
        points_3d (numpy.ndarray): Triangulated 3D points (N, 3).

    Returns:
        o3d.geometry.PointCloud: Sparse point cloud.
    """
    point_cloud = o3d.geometry.PointCloud()
    point_cloud.points = o3d.utility.Vector3dVector(points_3d)
    return point_cloud

# Generate and visualize sparse point cloud
sparse_cloud = generate_sparse_point_cloud(points_3d)
o3d.visualization.draw_geometries([sparse_cloud])

--- Dhruv

One-view reconstruction

depth_maps = []
images = []
for i in range(len(rgb_paths)):
    rgb_image = cv2.imread(undistorted_images[i])
    depth_map = cv2.imread(depth_paths[i], cv2.IMREAD_GRAYSCALE)
    depth_maps.append(depth_map)
    images.append(rgb_image)

Relate depth values to Z-coordinate

def get_depth_for_features(feature_correspondence_matrix, depth_maps):
    depth_values = []

    for image_index, feature_points in enumerate(feature_correspondence_matrix):
        image_depth_values = []
        depth_map = depth_maps[image_index]

        for point in feature_points:
            if np.array_equal(point, [-1, -1]): 
                image_depth_values.append(None)
            else:
                u, v = point
                depth_value = depth_map[u, v]  
                image_depth_values.append(depth_value)

        depth_values.append(image_depth_values)

    return depth_values

depth_values = get_depth_for_features(feature_correspondence_matrix, depth_maps)

for image_index, image_depth_values in enumerate(depth_values):
    print(f"Image {image_index}:")
    for feature_index, depth in enumerate(image_depth_values):
        print(f"  Feature {feature_index}: Depth (0-255 scale) = {depth}")

Image 0:
  Feature 0: Depth (0-255 scale) = 204
  Feature 1: Depth (0-255 scale) = 160
  Feature 2: Depth (0-255 scale) = 190
  Feature 3: Depth (0-255 scale) = 193
  Feature 4: Depth (0-255 scale) = 190
  Feature 5: Depth (0-255 scale) = 167
  Feature 6: Depth (0-255 scale) = 204
Image 1:
  Feature 0: Depth (0-255 scale) = 163
  Feature 1: Depth (0-255 scale) = 150
  Feature 2: Depth (0-255 scale) = 150
  Feature 3: Depth (0-255 scale) = 147
  Feature 4: Depth (0-255 scale) = 200
  Feature 5: Depth (0-255 scale) = 186
  Feature 6: Depth (0-255 scale) = 160
Image 2:
  Feature 0: Depth (0-255 scale) = 237
  Feature 1: Depth (0-255 scale) = 196
  Feature 2: Depth (0-255 scale) = None
  Feature 3: Depth (0-255 scale) = 237
  Feature 4: Depth (0-255 scale) = None
  Feature 5: Depth (0-255 scale) = 167
  Feature 6: Depth (0-255 scale) = 247
Image 3:
  Feature 0: Depth (0-255 scale) = 200
  Feature 1: Depth (0-255 scale) = None
  Feature 2: Depth (0-255 scale) = 165
  Feature 3: Depth (0-255 scale) = 194
  Feature 4: Depth (0-255 scale) = None
  Feature 5: Depth (0-255 scale) = 155
  Feature 6: Depth (0-255 scale) = 190
Image 4:
  Feature 0: Depth (0-255 scale) = 161
  Feature 1: Depth (0-255 scale) = 130
  Feature 2: Depth (0-255 scale) = 128
  Feature 3: Depth (0-255 scale) = 151
  Feature 4: Depth (0-255 scale) = None
  Feature 5: Depth (0-255 scale) = 175
  Feature 6: Depth (0-255 scale) = 149
Image 5:
  Feature 0: Depth (0-255 scale) = 249
  Feature 1: Depth (0-255 scale) = None
  Feature 2: Depth (0-255 scale) = None
  Feature 3: Depth (0-255 scale) = 249
  Feature 4: Depth (0-255 scale) = None
  Feature 5: Depth (0-255 scale) = 166
  Feature 6: Depth (0-255 scale) = 249
Image 6:
  Feature 0: Depth (0-255 scale) = 208
  Feature 1: Depth (0-255 scale) = 179
  Feature 2: Depth (0-255 scale) = 206
  Feature 3: Depth (0-255 scale) = 205
  Feature 4: Depth (0-255 scale) = 207
  Feature 5: Depth (0-255 scale) = 180
  Feature 6: Depth (0-255 scale) = 214
Image 7:
  Feature 0: Depth (0-255 scale) = None
  Feature 1: Depth (0-255 scale) = None
  Feature 2: Depth (0-255 scale) = None
  Feature 3: Depth (0-255 scale) = None
  Feature 4: Depth (0-255 scale) = 234
  Feature 5: Depth (0-255 scale) = 198
  Feature 6: Depth (0-255 scale) = None
Image 8:
  Feature 0: Depth (0-255 scale) = None
  Feature 1: Depth (0-255 scale) = 206
  Feature 2: Depth (0-255 scale) = 242
  Feature 3: Depth (0-255 scale) = None
  Feature 4: Depth (0-255 scale) = None
  Feature 5: Depth (0-255 scale) = 162
  Feature 6: Depth (0-255 scale) = 231

def get_point_depth_in_view(point, view_idx):
    depth_map = depth_maps[view_idx]
    depth_value = depth_map[point[0], point[1]]
    return depth_value

Generate pixel coordinate datasets for point cloud

dataset_height = range(1, 551, 2)
dataset_width = range(1, 881, 2)
dataset_coordinates = []

for i in range(len(dataset_height)):
    for j in range(len(dataset_width)):
        dataset_coordinates.append([dataset_height[i], dataset_width[j]])

#print(dataset_coordinates)
print(len(dataset_coordinates))

121000

Calculate 3D coordinates for the generated point dataset

for view 0

def get_depths(points):
    depths = []
    for i in range(len(points)):
        pixel_depth = get_point_depth_in_view(points[i], 0)
        if pixel_depth == 255 or pixel_depth == 0:
            depths.append(-1)
        else:
            depth = points_3d[0][2] * pixel_depth / get_point_depth_in_view(feature_correspondence_matrix[0][0], 0)
            depths.append(depth)
    return depths

dataset_z = get_depths(dataset_coordinates)
#print(dataset_z)

dataset_3d = []
for i in range(len(dataset_coordinates)):
    z = dataset_z[i]
    if (z == -1):
        continue

    x = (dataset_coordinates[i][0] - principal_point[1]) / focal_length_px * z
    y = (dataset_coordinates[i][1] - principal_point[0]) / focal_length_px * z
    dataset_3d.append([x, y, z])

#print(dataset_3d[:5])

Extract colours for the selected points

def get_point_colour_in_view(point, view_idx):
    colour_value = images[0][point[0]][point[1]]
    return colour_value

dataset_colours = []
for i in range(len(dataset_coordinates)):
    z = dataset_z[i]
    if (z == -1):
        continue
    colour = get_point_colour_in_view(dataset_coordinates[i], 0)
    dataset_colours.append(colour)

Get mesh via utility function!

def ply_creator(input_3d, rgb_data, filename):
    assert (input_3d.ndim == 2), "Pass 3d points as NumPointsX3 array "
    text1 = """ply\nformat ascii 1.0"""
    text2 = "element vertex " + str(input_3d.shape[0])
    text3 = """property float x
    property float y
    property float z
    property uchar red
    property uchar green
    property uchar blue
    end_header"""
    
    with open(filename, 'w') as ply_file:
        ply_file.write(text1 + "\n")
        ply_file.write(text2 + "\n")
        ply_file.write(text3 + "\n")
        for i in range(input_3d.shape[0]):
            ply_file.write(f"{input_3d[i, 0]} {input_3d[i, 1]} {input_3d[i, 2]} {rgb_data[i][2]} {rgb_data[i][1]} {rgb_data[i][0]}\n")

dataset_3d = np.array(dataset_3d)
dataset_colours = np.array(dataset_colours)
ply_creator(dataset_3d, dataset_colours, 'sparse_reconstruction.ply')

--- One-view reconstruction done by Daiana Tei

Dense Reconstruction

proceed here

Load Depth Maps, Calibration Data and Camera poses

import cv2
import numpy as np
import os

def load_depth_maps(depth_folder, max_depth=10.0):
    """
    Load and normalize depth maps from a folder.

    Args:
        depth_folder (str): Path to the folder containing depth images.
        max_depth (float): Maximum depth value for scaling.

    Returns:
        list of numpy.ndarray: List of depth maps (real-world scale).
    """
    depth_maps = []
    for filename in sorted(os.listdir(depth_folder)):
        if filename.endswith(".png"):
            # Load depth map as grayscale
            depth_map = cv2.imread(os.path.join(depth_folder, filename), cv2.IMREAD_GRAYSCALE)
            # Scale depth map to real-world depth
            depth_map = (depth_map.astype(np.float32) / 255.0) * max_depth
            depth_maps.append(depth_map)
    return depth_maps

# Example usage
depth_folder = "data/depths"
depth_maps = load_depth_maps(depth_folder)

depth_maps

[array([[10., 10., 10., ..., 10., 10., 10.],
        [10., 10., 10., ..., 10., 10., 10.],
        [10., 10., 10., ..., 10., 10., 10.],
        ...,
        [10., 10., 10., ..., 10., 10., 10.],
        [10., 10., 10., ..., 10., 10., 10.],
        [10., 10., 10., ..., 10., 10., 10.]],
       shape=(551, 881), dtype=float32),
 array([[10., 10., 10., ..., 10., 10., 10.],
        [10., 10., 10., ..., 10., 10., 10.],
        [10., 10., 10., ..., 10., 10., 10.],
        ...,
        [10., 10., 10., ..., 10., 10., 10.],
        [10., 10., 10., ..., 10., 10., 10.],
        [10., 10., 10., ..., 10., 10., 10.]],
       shape=(551, 881), dtype=float32),
 array([[10., 10., 10., ..., 10., 10., 10.],
        [10., 10., 10., ..., 10., 10., 10.],
        [10., 10., 10., ..., 10., 10., 10.],
        ...,
        [10., 10., 10., ..., 10., 10., 10.],
        [10., 10., 10., ..., 10., 10., 10.],
        [10., 10., 10., ..., 10., 10., 10.]],
       shape=(551, 881), dtype=float32),
 array([[10., 10., 10., ..., 10., 10., 10.],
        [10., 10., 10., ..., 10., 10., 10.],
        [10., 10., 10., ..., 10., 10., 10.],
        ...,
        [10., 10., 10., ..., 10., 10., 10.],
        [10., 10., 10., ..., 10., 10., 10.],
        [10., 10., 10., ..., 10., 10., 10.]],
       shape=(551, 881), dtype=float32),
 array([[10., 10., 10., ..., 10., 10., 10.],
        [10., 10., 10., ..., 10., 10., 10.],
        [10., 10., 10., ..., 10., 10., 10.],
        ...,
        [10., 10., 10., ..., 10., 10., 10.],
        [10., 10., 10., ..., 10., 10., 10.],
        [10., 10., 10., ..., 10., 10., 10.]],
       shape=(551, 881), dtype=float32),
 array([[10., 10., 10., ..., 10., 10., 10.],
        [10., 10., 10., ..., 10., 10., 10.],
        [10., 10., 10., ..., 10., 10., 10.],
        ...,
        [10., 10., 10., ..., 10., 10., 10.],
        [10., 10., 10., ..., 10., 10., 10.],
        [10., 10., 10., ..., 10., 10., 10.]],
       shape=(551, 881), dtype=float32),
 array([[10., 10., 10., ..., 10., 10., 10.],
        [10., 10., 10., ..., 10., 10., 10.],
        [10., 10., 10., ..., 10., 10., 10.],
        ...,
        [10., 10., 10., ..., 10., 10., 10.],
        [10., 10., 10., ..., 10., 10., 10.],
        [10., 10., 10., ..., 10., 10., 10.]],
       shape=(551, 881), dtype=float32),
 array([[10.       , 10.       , 10.       , ..., 10.       , 10.       ,
         10.       ],
        [10.       , 10.       , 10.       , ..., 10.       , 10.       ,
         10.       ],
        [10.       , 10.       , 10.       , ..., 10.       , 10.       ,
         10.       ],
        ...,
        [10.       , 10.       , 10.       , ...,  4.5882354,  4.5882354,
          4.5882354],
        [10.       , 10.       , 10.       , ...,  4.5882354,  4.5882354,
          4.5882354],
        [10.       , 10.       , 10.       , ...,  4.5882354,  4.5882354,
          4.5882354]], shape=(551, 881), dtype=float32),
 array([[10.       , 10.       , 10.       , ..., 10.       , 10.       ,
         10.       ],
        [10.       , 10.       , 10.       , ..., 10.       , 10.       ,
         10.       ],
        [10.       , 10.       , 10.       , ..., 10.       , 10.       ,
         10.       ],
        ...,
        [ 3.8039217,  3.8039217,  3.8039217, ..., 10.       , 10.       ,
         10.       ],
        [ 3.8039217,  3.8039217,  3.8039217, ..., 10.       , 10.       ,
         10.       ],
        [ 3.8039217,  3.8039217,  3.8039217, ..., 10.       , 10.       ,
         10.       ]], shape=(551, 881), dtype=float32)]

# Extract calibration parameters
calibration_data = np.load("data/camera_calibration.npy", allow_pickle=True).item()

# Construct the intrinsic matrix
focal_length_px = calibration_data["focal_length_px"]
principal_point = calibration_data["principal_point"]

intrinsics = np.array([
    [focal_length_px, 0, principal_point[0]],
    [0, focal_length_px, principal_point[1]],
    [0, 0, 1]
])

print("Constructed Intrinsic Matrix:\n", intrinsics)

Constructed Intrinsic Matrix:
 [[629.28571429   0.         275.        ]
 [  0.         629.28571429 440.        ]
 [  0.           0.           1.        ]]

# Load camera poses from file
poses = np.load("data/camera_movement.npy")
print("Camera Poses Shape:", poses.shape)  # Should be (N, 4, 4) for N views

Camera Poses Shape: (8, 4, 4)

Integrate Depth Maps

def integrate_depth_maps(depth_maps, intrinsics, poses):
    """
    Integrate depth maps into a dense point cloud.

    Args:
        depth_maps (list of numpy.ndarray): Depth maps for each view.
        intrinsics (numpy.ndarray): Camera intrinsic matrix.
        poses (list of numpy.ndarray): Camera pose matrices.

    Returns:
        numpy.ndarray: Dense 3D points (N, 3).
    """
    dense_points = []
    fx, fy, cx, cy = intrinsics[0, 0], intrinsics[1, 1], intrinsics[0, 2], intrinsics[1, 2]
    for depth_map, pose in zip(depth_maps, poses):
        h, w = depth_map.shape
        for y in range(h):
            for x in range(w):
                z = depth_map[y, x]
                if z > 0:  # Ignore invalid depth values
                    X_cam = np.array([(x - cx) * z / fx, (y - cy) * z / fy, z, 1])
                    X_world = np.dot(pose, X_cam)[:3]
                    dense_points.append(X_world)
    return np.array(dense_points)

# Integrate depth maps into a dense cloud
dense_points = integrate_depth_maps(depth_maps, intrinsics, poses)

# Combine sparse and dense points
combined_points = np.vstack([np.asarray(sparse_cloud.points), dense_points])

from scipy.spatial import Delaunay

def generate_mesh(points_3d):
    """
    Generate a surface mesh from 3D points using Delaunay triangulation.

    Args:
        points_3d (numpy.ndarray): 3D points (N, 3).

    Returns:
        tuple: (vertices, faces) of the generated mesh.
    """
    points_2d = points_3d[:, :2]
    tri = Delaunay(points_2d)
    vertices = points_3d
    faces = tri.simplices
    return vertices, faces

# Generate mesh
vertices, faces = generate_mesh(combined_points)

def save_mesh_to_ply(vertices, faces, filename="dense_reconstruction.ply"):
    """
    Save a mesh to a PLY file.

    Args:
        vertices (numpy.ndarray): Mesh vertices (N, 3).
        faces (numpy.ndarray): Mesh faces (M, 3).
        filename (str): Output filename.
    """
    with open(filename, "w") as f:
        f.write("ply\n")
        f.write("format ascii 1.0\n")
        f.write(f"element vertex {len(vertices)}\n")
        f.write("property float x\n")
        f.write("property float y\n")
        f.write("property float z\n")
        f.write(f"element face {len(faces)}\n")
        f.write("property list uchar int vertex_indices\n")
        f.write("end_header\n")
        for vertex in vertices:
            f.write(f"{vertex[0]} {vertex[1]} {vertex[2]}\n")
        for face in faces:
            f.write(f"3 {face[0]} {face[1]} {face[2]}\n")

# Save the mesh
save_mesh_to_ply(vertices, faces, "dense_reconstruction.ply")
print("Dense reconstruction saved as 'dense_reconstruction.ply'.")

Dense reconstruction saved as 'dense_reconstruction.ply'.